<div class="problemindexholder" problemindex="A">
 <div class="ttypography">
  <div class="problem-statement">
   <div class="header">
    <div class="title">
     A. Five Dimensional Points
    </div>
    <div class="time-limit">
     <div class="property-title">
      time limit per test
     </div>
     2 seconds
    </div>
    <div class="memory-limit">
     <div class="property-title">
      memory limit per test
     </div>
     256 megabytes
    </div>
    <div class="input-file">
     <div class="property-title">
      input
     </div>
     standard input
    </div>
    <div class="output-file">
     <div class="property-title">
      output
     </div>
     standard output
    </div>
   </div>
   <div>
    <p>
     You are given set of
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     points in 5-dimensional space. The points are labeled from
     <span class="tex-span">
      1
     </span>
     to
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     . No two points coincide.
    </p>
    <p>
     We will call point
     <span class="tex-span">
      <i>
       a
      </i>
     </span>
     <span class="tex-font-style-it">
      bad
     </span>
     if there are different points
     <span class="tex-span">
      <i>
       b
      </i>
     </span>
     and
     <span class="tex-span">
      <i>
       c
      </i>
     </span>
     , not equal to
     <span class="tex-span">
      <i>
       a
      </i>
     </span>
     , from the given set such that angle between vectors
     <img align="middle" class="tex-formula" src="/predownloaded/1f/5c/1f5c3126049e76eda0a26fa995e00df7fa317840.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     and
     <img align="middle" class="tex-formula" src="/predownloaded/94/2c/942cd02e0eb386e3096e69a0de98fb1ca360128b.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     is acute (i.e. strictly less than
     <img align="middle" class="tex-formula" src="/predownloaded/3d/f5/3df5d3c78b3bb193a6358528b4d185ca05e26551.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     ). Otherwise, the point is called
     <span class="tex-font-style-it">
      good
     </span>
     .
    </p>
    <p>
     The angle between vectors
     <img align="middle" class="tex-formula" src="/predownloaded/4e/21/4e219c5191ad791ba8b11eb6535cd4de40c0f282.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     and
     <img align="middle" class="tex-formula" src="/predownloaded/fd/30/fd301105137a48f091f435b320600a2dc5c7b51c.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     in 5-dimensional space is defined as
     <img align="middle" class="tex-formula" src="/predownloaded/66/68/6668f732ec0332ea0c9eaab1e8bf09f0a3eb4113.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     , where
     <img align="middle" class="tex-formula" src="/predownloaded/e5/5c/e55c3634e2a0882221216adad152a31d3d7c3c7a.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     is the scalar product and
     <img align="middle" class="tex-formula" src="/predownloaded/8b/6a/8b6abea61fb378b60657245d936e697cdc92405b.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     is length of
     <img align="middle" class="tex-formula" src="/predownloaded/4e/21/4e219c5191ad791ba8b11eb6535cd4de40c0f282.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     .
    </p>
    <p>
     Given the list of points, print the indices of the good points in ascending order.
    </p>
   </div>
   <div class="input-specification">
    <div class="section-title">
     Input
    </div>
    <p>
     The first line of input contains a single integer
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     (
     <span class="tex-span">
      1 ≤
      <i>
       n
      </i>
      ≤ 10
      <sup class="upper-index">
       3
      </sup>
     </span>
     ) — the number of points.
    </p>
    <p>
     The next
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     lines of input contain five integers
     <span class="tex-span">
      <i>
       a
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ,
      <i>
       b
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ,
      <i>
       c
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ,
      <i>
       d
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ,
      <i>
       e
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
     </span>
     (
     <span class="tex-span">
      |
      <i>
       a
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      |, |
      <i>
       b
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      |, |
      <i>
       c
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      |, |
      <i>
       d
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      |, |
      <i>
       e
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      | ≤ 10
      <sup class="upper-index">
       3
      </sup>
     </span>
     )  — the coordinates of the i-th point. All points are distinct.
    </p>
   </div>
   <div class="output-specification">
    <div class="section-title">
     Output
    </div>
    <p>
     First, print a single integer
     <span class="tex-span">
      <i>
       k
      </i>
     </span>
     — the number of good points.
    </p>
    <p>
     Then, print
     <span class="tex-span">
      <i>
       k
      </i>
     </span>
     integers, each on their own line — the indices of the good points in ascending order.
    </p>
   </div>
   <div class="sample-tests">
    <div class="section-title">
     Examples
    </div>
    <div class="sample-test">
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>6<br/>0 0 0 0 0<br/>1 0 0 0 0<br/>0 1 0 0 0<br/>0 0 1 0 0<br/>0 0 0 1 0<br/>0 0 0 0 1<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>1<br/>1<br/></pre>
     </div>
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>3<br/>0 0 1 2 0<br/>0 0 9 2 0<br/>0 0 5 9 0<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>0<br/></pre>
     </div>
    </div>
   </div>
   <div class="note">
    <div class="section-title">
     Note
    </div>
    <p>
     In the first sample, the first point forms exactly a
     <img align="middle" class="tex-formula" src="/predownloaded/3d/f5/3df5d3c78b3bb193a6358528b4d185ca05e26551.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     angle with all other pairs of points, so it is good.
    </p>
    <p>
     In the second sample, along the cd plane, we can see the points look as follows:
    </p>
    <p>
     <img class="tex-graphics" src="/predownloaded/fd/e3/fde3e8cbbf2eacf24cb8342bfa6d2e956a1c4739.png" style="max-width: 100.0%;max-height: 100.0%;"/>
    </p>
    <p>
     We can see that all angles here are acute, so no points are good.
    </p>
   </div>
  </div>
  <p>
  </p>
 </div>
</div>
